[Clear1nsight]

Change and mathematical scope

Assignment C derives required changed transports and productive helper endpoints from PR4470's chronological words, independently of the physical recipe inventory. All 406 new transport pairs and 17 distinct helper boundaries match the 423 exact physical recipes in both orientations. All 408 helper owners are represented. No new kappa or selected-frontier change.

Each orientation contains 3,302 persistent transport occurrences over 2,856 distinct pairs. Of those occurrences, 439 have directly audited recipes and 2,863 are explicitly inherited. The 240 retained warp events and eight owned-centre jobs are separately classified. Thus this closes the changed/helper coverage boundary without falsely claiming a fresh physical audit of every retained operation.

Canonical subspaces and exact reference-basis embeddings are both retained in the join. Equal spans do not silently licence a phase-changing frame replacement. The original pinned constructor emits data only; its proof engines and the predecessor matrix checker are not imported.

Task and overlap

Canonical base f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc, priority revision 7, unchanged at final refresh. PR4470 source b9a13c1673e0e9697de410de16e8bbf3207a7363; fork PR14 at af86fb28f4fe039d4bb8419850af99a6fc474587 supplies the retained matrix receipt. Eight exact sources are authenticated by Git blob and SHA256. The receipt's source and ordered pair/rank/orientation digest bind its reuse, not a fresh matrix execution.

PR4504 covers chronological frames and billing; PR4478 covers arithmetic; PR4457 covers predecessor operators. The final refresh found PR4539's independent noncommuting p16 free-algebra replay of PR4534. That is valuable complementary controller evidence but does not discharge the physical query/owner caller left here. Targeted searches and bounded Discussion reading are not exhaustive overlap coverage. TASK.json declares the refined independent-moment scope; the historical baseline helper was not run.

This fork-only PR targets the isolated current-main contribution base. No main merge, upstream submission or frontier promotion.

Validation

Final-head registered workflow 39725302242 passes at 6034837daf958effc42a1908f1b3e97fe6072d0b. Onboarding, package metadata/source authentication, normal full coverage join, optimised controls and preservation of committed inputs pass on Ubuntu with CPython 3.12.15, standard library only.

RESULT.json retains every observed scientific field. The exact set comparison rejects missing or extra changed/helper coverage. An actual oriented record is deliberately removed and rejected. Four positive and seven rejection controls cover canonicalisation, basis embeddings, duplicates, false ranks, missing orientation/coverage and dependent bases.

python -B scripts/research_package.py --package research/pr4470-coverage-join
python -I -O -B research/pr4470-coverage-join/verify.py --self-test

The full 632-input operator endpoint, inherited physical transports/warps/centres, p16 query/owner/erasure protocol, precision/stock and outer theorem remain separate. Counting owned clears is not a full semantic erasure proof. No new matrix replay, complete selected cold replay, optional source-history preflight, independent human or formal-kernel verification is claimed.

Credit

Credit Cinna Davis's PR4470 constructor, zxv's receiver/native/controller work, Jacob Alan Sussman's recursion, Mihir Srivastava's PR4504, Mark/Matarener, Ryanson Jonathan and all retained scalar/Clifford/geometry/BIT/outer notices. Prior fork PR14 matrix evidence and this join were prepared for Chris R / Clear1nsight with substantial OpenAI assistance, Apache-2.0. Separate workstreams in one session are not separately launched agents.

Open next questions

Use the executed classification to bind the smallest inherited operator family to exact retained evidence. Then audit the complete arbitrary-input invocation and actual p16 copied-query/owner/erasure caller, using the new PR4534/4539 formal evidence only within its stated scope. Do not repeat the 423 matrix calculations or root arithmetic as though they were missing. README.md, TASK.json and the public handoff identify first steps and blockers.

[Clear1nsight]

HANDOFF — changed-pair coverage closed; inherited operators and physical caller remain

Status on 22 October 2026, priority revision 7. Assignment C is complete at 6034837daf958effc42a1908f1b3e97fe6072d0b, with final-head registered workflow 39725302242 passing. The next tasks are unclaimed. This is separately implemented AI-assisted evidence, not human or proof-kernel acceptance.

The event-derived required set equals all 423 physical recipes in both orientations: 406 new transport pairs and 17 distinct helper boundaries representing 408 owners. Each orientation has 439 directly covered chronological transport occurrences and 2,863 inherited occurrences. The 240 retained warps and eight centre jobs are explicitly outside fresh physical coverage. Exact source bytes and the oriented index bind this result to fork PR14's unchanged successful matrix receipt; those matrices were reused, not rerun.

The smallest useful next task is to bind one inherited operator family from this classification to exact retained evidence. A further distinct task is the complete 632-arbitrary-input invocation with owned-centre restoration, followed by the actual p16 copied-query/owner/erasure protocol. Stop at one interface rather than claiming a full supplier from pairwise correctness. Missing coverage, wrong orientation, embedding/phase mismatch and duplicate ownership remain required controls.

Canonical main was refreshed and remains f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc; PR4470 remains pinned at b9a13c1673e0e9697de410de16e8bbf3207a7363. The final refresh found PR4534/4539's noncommuting formal controller work, which can support the next caller audit but does not itself implement physical operators. PR4478 arithmetic and PR4504 frame/billing coverage should not be repeated as missing work.

Reproduce with python -B scripts/research_package.py --package research/pr4470-coverage-join. The package preserves its source pins, complete receipt and optimised controls. Precision/stock, physical implementation costs and outer transfer remain outside scope. No selected cold replay, source-history preflight, upstream PR, merge or frontier change was performed.

Credit Cinna Davis, zxv, Jacob Alan Sussman, Mihir Srivastava, Mark/Matarener, Ryanson Jonathan and retained notices. Prepared for Chris R / Clear1nsight with substantial OpenAI assistance. This public fork handoff has not been cross-posted to central Discussion CrocSwap#1166 because the available connector lacks Discussion-comment writes.

{"schema":"integer-mult-coordination/v1","kind":"HANDOFF","task":"independent-moment","scope":"Bind one inherited PR4470 operator family to exact evidence, then isolate the complete native endpoint and physical p16 query/owner protocol","base":"f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc","expiry":null,"artifact":"https://github.com/Clear1nsight/integer-mult-bounds/commit/6034837daf958effc42a1908f1b3e97fe6072d0b"}